Impact of First-order Electroweak Phase Transition on QCD Axion

The QCD axion addresses the strong CP problem and dark matter via the misalignment mechanism, typically requiring a decay constant $f_a\sim \mathcal{O}(10^{12}$ GeV), unless the initial misalignment angle ($\theta_i$) is fine-tuned. This work presents a novel approach where the possibility that the QCD axion satisfying the correct relic is extended over a broad range for $f_a\in [10^8, 10^{14}$] GeV without fine-tuning the $\theta_i$, by introducing a new phase of axion oscillation dynamics across the electroweak phase transition (EWPT). This mechanism, we call it {\it{recurrent ~misalignment}}, is a result of a non-renormalizable Peccei-Quinn symmetry breaking interaction involving the axion and the sector responsible for making the EWPT of first order. The scenario not only enhances the QCD axion parameter space in terms of its detection possibility, but also provides a unique probe by detectable gravitational waves.